On the minimum number of minimal codewords
Romar dela Cruz, Michael Kiermaier, Sascha Kurz, Alfred Wassermann
TL;DR
This paper investigates the lower bounds on the number of minimal codewords in linear codes using projective geometry, providing bounds, exact values in some cases, and extending to minimal subcode supports.
Contribution
It introduces new bounds and exact values for minimal codewords in linear codes and extends the analysis to minimal subcode supports.
Findings
Derived bounds for minimal codewords
Determined exact values in specific cases
Extended analysis to minimal subcode supports
Abstract
We study the minimum number of minimal codewords in linear codes from the point of view of projective geometry. We derive bounds and in some cases determine the exact values. We also present an extension to minimal subcode supports.
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Taxonomy
TopicsCoding theory and cryptography · graph theory and CDMA systems · Interconnection Networks and Systems